Cross-Vehicle 3D Geometric Consistency for Self-Supervised Surround Depth Estimation on Articulated Vehicles

Weimin Liu; Jiyuan Qiu; Wenjun Wang; Joshua H. Meng

cs.CVApr 3, 2026

Cross-Vehicle 3D Geometric Consistency for Self-Supervised Surround Depth Estimation on Articulated Vehicles

Authors: Weimin Liu, Jiyuan Qiu, Wenjun Wang, Joshua H. Meng

Organizations: School of vehicle and Mobility, Tsinghua University, Beijing, China · Remote Sensing and Earth Observation Laboratory, University of Copenhagen, Copenhagen K, Denmark · California PATH, University of California, Berkeley, CA, USA

Abstract

Surround depth estimation provides a cost-effective alternative to LiDAR for 3D perception in autonomous driving. While recent self-supervised methods explore multi-camera settings to improve scale awareness and scene coverage, they are primarily designed for passenger vehicles and rarely consider articulated vehicles or robotics platforms. The articulated structure introduces complex cross-segment geometry and motion coupling, making consistent depth reasoning across views more challenging. In this work, we propose ArticuSurDepth, a self-supervised framework for surround-view depth estimation on articulated vehicles that enhances depth learning through cross-view and cross-vehicle geometric consistency guided by structural priors from vision foundation model. Specifically, we introduce multi-view spatial context enrichment strategy and a cross-view surface normal constraint to improve structural coherence across spatial and temporal contexts. We further incorporate camera height regularization with ground plane-awareness to encourage metric depth estimation, together with cross-vehicle pose consistency that bridges motion estimation between articulated segments. To validate our proposed method, an articulated vehicle experiment platform was established with a dataset collected over it. Experiment results demonstrate state-of-the-art (SoTA) performance of depth estimation on our self-collected dataset as well as on DDAD, nuScenes, and KITTI benchmarks.

Figures & tables

Fig. 1 : Surround depth estimation for articulated vehicle.

Fig. 2 : Overview: (a) Network architecture of ArticuSurDepth; (b) Self-supervised training framework and its loss components: (Left) Within- and cross-vehicle spatial context enrichment. Example: for the target view $C_{5}$ , the within-vehicle right view is $C_{6}$ , while the type-2 cross-vehicle right view is $C_{0}$ . (Right) Cross-view pseudo surface normal consistency ( $\mathcal{L}_{\text{PNC}}$ ).

Fig. 3 : Example of cross-vehicle extrinsics calibration: (a) LiDAR pointclouds registration; (b) Pointclouds of $\mathcal{L}_{f}$ projected on camera $C_{6}$ (mounted on front vehicle); (c) Pointclouds of $\mathcal{L}_{r}$ projected on camera $C_{6}$ ; (d) Within- and cross-vehicle spatial contexts and transformations.

Fig. 4 : Example of spatial warps: (a) Color image of $C_{5}$ ; (b) Spatial warp from left camera $C_{9}$ ; (c) Spatial cross-vehicle warp (type-2) from left camera $C_{2}$ ; (d) Spatial cross-vehicle warp (type-2) from right camera $C_{3}$ .

Type	Camera pairs
Type-0	$(C_{8}\&C_{2})$ , $(C_{7}\&C_{3})$
Type-1	$(C_{9}\&C_{2})$ , $(C_{6}\&C_{3})$ , $(C_{8}\&C_{1})$ , $(C_{7}\&C_{4})$
Type-2	$(C_{5}\&C_{2})$ , $(C_{5}\&C_{3})$ , $(C_{9}\&C_{1})$ , $(C_{6}\&C_{4})$ , $(C_{8}\&C_{0})$ , $(C_{7}\&C_{0})$

TABLE I : List of camera pairs for cross-vehicle spatial contexts.

Fig. 5 : Comparison of depth and direct interpolation-based surface normal reprojection method. PSN implies pseudo surface normal. ST implies spatial-temporal context.

Fig. 6 : (a) Within- and (b) cross-vehicle pose consistency.

Fig. 7 : Our self-established experiment platform.

Fig. 8 : Self-occlusion masks overlaid on images: (a) $C_{2}$ , (b) $C_{3}$ , (c) $C_{7}$ , (d) $C_{8}$ are four cameras that have visible occlusion components on the other vehicle under certain motion cases.

Fig. 9 : Visualization on val split: (a) Examples of depth and surface normal estimation on self-collected dataset; (b) Example of surround-view depth estimation on test split of self-collected dataset; (c) Examples of direct inference on DDAD; (d) Examples of direct inference on nuScenes.

KITTI [ 20 ] (192 $\times$ 640)
Method	Abs Rel $\downarrow$	Sq Rel $\downarrow$	RMSE $\downarrow$	RMSE ${}_{\text{log}}$ $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
MonoViT [ 23 ]	0.099	0.708	4.372	0.175	0.900	0.967	0.984
EDS-Depth [ 24 ]	0.095	0.619	4.184	0.170	0.905	0.969	0.985
GeoDepth [ 10 ]	0.094	0.641	4.175	0.167	0.906	0.970	0.986
Ours ${\dagger}$	0.094	0.628	4.134	0.165	0.908	0.971	0.986
DDAD [ 21 ] (384 $\times$ 640)

TABLE II : Depth estimation on KITTI [ 20 ] , DDAD [ 21 ] , nuScenes [ 22 ] and our own self-collected datasets (Results on KITTI are scale-ambiguous evaluation.

{\dagger}

indicates our modified GeoDepth or GeoSurDepth with proposed losses. # implies reproduced results by VFDepth [ 7 ] . * indicates modified framework for adaptation to articulated vehicle pattern. Results best in bold , second best underlined ).

$S_{0}$	$S_{1}$	$S_{2}$	Abs Rel $\downarrow$	Sq Rel $\downarrow$	RMSE $\downarrow$	RMSE ${}_{\text{log}}$ $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
✗	✗	✗	0.192	1.235	6.237	0.259	0.656	0.921	0.973
✓	✗	✗	0.190	1.193	6.069	0.255	0.661	0.926	0.975
✗	✓	✗	0.187	1.165	5.983	0.251	0.667	0.929	0.976
✗	✗	✓	0.188	1.173	5.992	0.252	0.666	0.929	0.975
✓	✓	✓	0.185	1.153	5.973	0.250	0.670	0.931	0.976

TABLE III : Ablation study on cross-vehicle context enrichment (

S_{i}

indicate type-

i

cross-vehicle spatial contexts).

Method	Abs Rel $\downarrow$	Sq Rel $\downarrow$	RMSE $\downarrow$	RMSE ${}_{\text{log}}$ $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
w/o $\mathcal{L}_{\text{PNC}}$	0.189	1.173	6.000	0.253	0.664	0.928	0.976
with $\tilde{\mathcal{L}}_{\text{NC}}$	0.186	1.162	5.981	0.250	0.668	0.930	0.976
Ours	0.185	1.153	5.973	0.250	0.670	0.931	0.976

TABLE IV : Ablation study on cross-view SN consistency (“D” indicates depth interpolation-based SN reprojection.

Fig. 10 : Example of ground plane detection or estimation, and camera height estimation (range of camera height estimation has been clipped for visualization).

Method	Abs Rel $\downarrow$	Sq Rel $\downarrow$	RMSE $\downarrow$	RMSE ${}_{\text{log}}$ $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
w/o $\mathcal{L}_{\text{CH}}$	0.189	1.254	6.229	0.258	0.667	0.921	0.973
with $\hat{\boldsymbol{\mathcal{M}}}_{g}$	0.202	1.454	6.491	0.268	0.640	0.911	0.969
Ours	0.185	1.153	5.973	0.250	0.670	0.931	0.976

TABLE V : Ablation study on ground-plane aware camera height regularization (

\hat{\boldsymbol{\mathcal{M}}}_{g}

indicates ground-plane detected with estimated depth and surface normal).

Method	Abs Rel $\downarrow$		$\delta_{1}$ $\uparrow$
Method	$J_{f}-J_{r}$	$C_{6}-C_{4}$	$J_{f}-J_{r}$	$C_{6}-C_{4}$
w / w.o $\mathcal{L}_{\text{VPC}}$	0.185 / 0.188	0.187 / 0.189	0.670 / 0.665	0.665 / 0.664

TABLE VI : Ablation study on cross-vehicle pose consistency.

Self-Supervised Monocular Depth Estimation

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CrossDepth: Geometry-Constrained Attention for Generalizable Multi-View Surround Depth Estimation
Sep 4, 2026Samer Abualhanud, Max MehltretterCross-View Attention Multi-View Depth Estimation
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Jun 15, 2026Shuai Yuan, Runxi Tang, Yuzhou Ji +8Multi-View Depth Estimation Multi-View Consistency
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Jun 14, 2026Yuanye Liu, Ke Zhang, Junzhe Jiang +3Depth Estimation Monocular Depth Estimation
Fudan University, Shanghai, China · Johns Hopkins University, Baltimore, USA

Sep 4, 2026J/K move · Enter open · S save

CrossDepth: Geometry-Constrained Attention for Generalizable Multi-View Surround Depth Estimation

Samer Abualhanud, Max Mehltretter

Leibniz University Hannover Hannover, Germany

Cross-View Attention Multi-View Depth Estimation Autonomous Driving Perception Multi-View Consistency Cross-Attention

Open paper AskPDF arXiv

Reliable 3D understanding of the surrounding environment is a core requirement for autonomous driving. Multi-view surround camera rigs provide broad scene coverage, but the spatially adjacent images typically overlap only minimally. Consequently, the depth of most pixels must be inferred from monocular appearance cues. These cues can appear differently across images and may therefore be interpreted differently by the depth estimation model. We target two main sources of cross-image inconsistency: differences in camera intrinsics and the limited receptive field of each image. We address the former by conditioning the features on per-pixel camera-aware ray embeddings, enabling the network to account for camera-dependent variations in monocular cues. We address the latter by extending each pixel's context beyond its own image through cross-image attention constrained to geometrically plausible regions, derived from the calibrated rig setup. The model is trained in a fully self-supervised manner based on photometric consistency. Evaluations on DDAD and nuScenes show improved overall depth accuracy and cross-image depth consistency over state-of-the-art self-supervised methods under in-domain and cross-domain evaluation. Code is available at https://abualhanud.github.io/CrossDepthPage/.

Abstract

Self-Supervised Monocular Depth Estimation

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